Question: Solve for $x$ and $y$ using elimination. ${5x-y = 18}$ ${4x+y = 27}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $9x = 45$ $\dfrac{9x}{{9}} = \dfrac{45}{{9}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {5x-y = 18}\thinspace$ to find $y$ ${5}{(5)}{ - y = 18}$ $25-y = 18$ $25{-25} - y = 18{-25}$ $-y = -7$ $\dfrac{-y}{{-1}} = \dfrac{-7}{{-1}}$ ${y = 7}$ You can also plug ${x = 5}$ into $\thinspace {4x+y = 27}\thinspace$ and get the same answer for $y$ : ${4}{(5)}{ + y = 27}$ ${y = 7}$